Least Common Multiple (LCM) of 109 and 61
The least common multiple (LCM) of 109 and 61 is 6649.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 109 and 61?
First, calculate the GCD of 109 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 61 = 1 remainder 48 |
| 2 | 61 ÷ 48 = 1 remainder 13 |
| 3 | 48 ÷ 13 = 3 remainder 9 |
| 4 | 13 ÷ 9 = 1 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 77 | 1309 |
| 197 and 155 | 30535 |
| 142 and 87 | 12354 |
| 36 and 146 | 2628 |
| 175 and 111 | 19425 |